derivative of (x^2-4/(x+0.5))

解答

\frac{d}{d x} (\frac{x ^{2} - 4}{x + 0.5})

\frac{x ^{2} + x + 4}{( x + 0.5 ) ^{2}}

求解步骤

\frac{d}{d x} (\frac{x ^{2} - 4}{x + 0.5})

使用微分除法定则:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( x ^{2} - 4 ) ( x + 0.5 ) - \frac{d}{d x} ( x + 0.5 ) ( x ^{2} - 4 )}{( x + 0.5 ) ^{2}}

\frac{d}{d x} (x^{2} - 4) = 2 x

\frac{d}{d x} (x + 0.5) = 1

= \frac{2 x ( x + 0.5 ) - 1 \cdot ( x ^{2} - 4 )}{( x + 0.5 ) ^{2}}

化简

\frac{2 x ( x + 0.5 ) - 1 \cdot ( x ^{2} - 4 )}{( x + 0.5 ) ^{2}} : \frac{x ^{2} + x + 4}{( x + 0.5 ) ^{2}}

= \frac{x ^{2} + x + 4}{( x + 0.5 ) ^{2}}

y \to 0 lim (a x^{2} + b x^{3})

d er i v a t i v e f (x) = 2 e^{x} (cos (x) - sin (x))

s l o p e in t erce pt (3, 4), (5, - 4)

\int \frac{5 e ^{2 x}}{e ^{2 x} + 11 e ^{x} + 24} d x

\frac{d}{d x} (x^{2} + 5 x + 4)